Nonlinear Dynamic Phenomena in Mechanics

  • Jerzy Warminski
  • Stefano Lenci
  • Matthew P. Cartmell
  • Giuseppe Rega
  • Marian Wiercigroch

Part of the Solid Mechanics and Its Applications book series (SMIA, volume 181)

Table of contents

  1. Front Matter
  2. Stefano Lenci, Laura Marcheggiani
    Pages 63-114
  3. Matthew P. Cartmell, Arkadiusz J. Żak, Olga A. Ganilova
    Pages 115-158
  4. Marian Wiercigroch, Ekaterina Pavlovskaia
    Pages 211-273
  5. Back Matter

About this book


Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses.

This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems.

Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinearities introduced by pendulum motion may change the system dynamics, and entail a rapid increase of the oscillations of both the structure and the pendulum, leading to full pendulum rotation or chaotic dynamics. To magnetorheological damping is proposed.

Nonlinear mechanics has to be used to explain undesired response in slender footbridges, such as that occurred in the famous event of the London Millenium Bridge. The observed phenomena can be explained by an analytical nonlinear discrete-time model.

Shape memory alloys (SMAs) exhibit very interesting nonlinear thermo-mechanical properties such as shape memory effect and superelasticity. SMA elements integrated within composite beams or plates can be used for active modification of structure properties e.g. by affecting their natural frequencies.

Finite amplitude, resonant, forced dynamics of sagged, horizontal or inclined, elastic cables have recently undergone meaningful research advances concerned with modelling, analysis, response, and nonlinear/nonregular phenomena. A variety of features of nonlinear multimodal interaction in different resonance conditions are comparatively addressed.

Non-smooth systems are very common in engineering practice. Three mechanical engineering problems are presented: (i) a vibro-impact system in the form of a moling device, (ii) the influence of the opening and closing of a fatigue crack on the host system dynamics, and (iii) nonlinear interactions between a rotor and snubber ring system.  

This book is aimed at a wide audience of engineers and researchers working in the field of nonlinear structural vibrations and dynamics, and undergraduate and postgraduate students reading mechanical, aerospace and civil engineering.

Editors and affiliations

  • Jerzy Warminski
    • 1
  • Stefano Lenci
    • 2
  • Matthew P. Cartmell
    • 3
  • Giuseppe Rega
    • 4
  • Marian Wiercigroch
    • 5
  1. 1.Lublin University of TechnologyLublinPoland
  2. 2.Department of Architecture, Buildings and StructuresPolytechnic University of MarcheAnconaItaly
  3. 3.School of EngineeringUniversity of GlasgowGlasgowUnited Kingdom
  4. 4.Department of Structural and Geotechnical EngineeringSapienza University of RomeRomaItaly
  5. 5.School of Engineering, Centre for Applied Dynamics Research (CADR) King’s College Research (CADR)University of AberdeenAberdeenUnited Kingdom

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 2012
  • Publisher Name Springer, Dordrecht
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-94-007-2472-3
  • Online ISBN 978-94-007-2473-0
  • Series Print ISSN 0925-0042
  • Buy this book on publisher's site